Almost-LCA in Tree

Revision en2, by skxqks, 2019-11-20 02:02:42

Is there a simple solution to the below problem in $$$O(1)$$$ per query with reasonable, such as $$$O(NlogN)$$$, preprocessing?

Problem: Given two nodes $$$u$$$ and $$$v$$$ in a tree, find the second node on the path from $$$u$$$ to $$$v$$$.

If $$$u$$$ is not an ancestor of $$$v$$$ this is easy. If $$$u$$$ is an ancestor of $$$v$$$ though then the answer is one of the children of $$$u$$$. You could compute the answer with jump-pointers in $$$O(log N)$$$ per query, but is there any easy way to find it in $$$O(1)$$$ per query?

Tags trees, data structures

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  Rev. Lang. By When Δ Comment
en2 English skxqks 2019-11-20 02:02:42 92
en1 English skxqks 2019-11-20 02:01:22 433 Initial revision (published)